Can you use a face to slice other faces?
There are two methods that are standing out to me. 

One is the boolean modifier. For this, you need to make the crystalline structures a separate object. Than add a boolean modifier to one of the objects and use the union type. This will actually join the objects, the downsides are that it can create sloppy topology so it really depends on how willing you are to have n-gons and triangles in your mesh.

The other one is the intersect tool which is new with 2.72. For this you need to be in edit mode and have everything selected. The easiest way to find it is to use the spacebar search menu. Just search "intersect".

Here's a demo on the intersect tool:
link

This won't join the two meshes like the boolean modifier, but instead it puts the verts where they need to be and leaves the user up to deciding what to do with the mesh.

I hope this helps.